Revealing mistake: The "hand" holding the gun rotates 180 degrees while the shooter's point of view does not move. A real hand can't reproduce that motion without moving extremely close to the face.
Continuity mistake: Immediately after the (Dali) dream sequence, when Dr. Brulov and Constance are reviewing Constance's notes, Dr. Brulov draws a pencil out of his coat pocket. Hitchcock then cuts to a close-up, and Dr. Brulov repeats the motion.
Continuity mistake: During Ingrid Bergman's first scene, she is having a psychiatric session with a patient. Suddenly, you hear the sound of the door opening. The camera immediately goes to the door, showing two men standing side by side, both perfectly still and standing in a place that would have required more movement than the time allotted between shot changes.